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Register a new userEfficient Computation of Expectations under Spanning Tree Distributions
حساب فعال للتوقعات تحت توزيعات الأشجار
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الملخص، نعطي إطارا عاما للاستنتاج في نماذج الأشجار الممتدة. نقترح خوارزميات موحدة للحالات المهمة من توقعات الترتيب الأول وتوقعات الترتيب الثاني في نماذج الأشجار ذات العوامل الواردة في الحافة وغير المشروعة. تستغل الخوارزميات الخاصة بنا اتصالا أساسيا بين التدرجات والتوقعات، مما يسمح لنا بالتخلص من الخوارزميات الفعالة. هذه الخوارزميات سهلة تنفيذها مع أو بدون برنامج التفريق التلقائي. نقوم بحفز تطوير إطار عملنا مع العديد من القصص الحذرية للبحث السابق، والتي طورت العديد من الخوارزميات غير الفعالة لتحسين توقعات الحوسبة وتدراجيها. نوضح كيف يحسب إطار عملنا بكفاءة العديد من الكميات مع الخوارزميات المعروفة، بما في ذلك درجة المرفقات المتوقعة ومعايير التركيبية والتوقعات المعممة. ككافأة، نعطي خوارزميات للكميات المفقودة في الأدب، بما في ذلك اختلاف KL. في جميع الحالات، يطابق نهجنا من كفاءة الخوارزميات القائمة، وفي عدة حالات، يقلل من تعقيد وقت التشغيل بعامل طول الجملة. نحن نقوم بالتحقق من تنفيذ إطار عملنا من خلال تجارب وقت التشغيل. نجد خوارزمياتنا تصل إلى 15 و 9 مرات أسرع من الخوارزميات السابقة لحساب شانون الانتروبيا وتدرج هدف التوقع المعمم، على التوالي.
Abstract We give a general framework for inference in spanning tree models. We propose unified algorithms for the important cases of first-order expectations and second-order expectations in edge-factored, non-projective spanning-tree models. Our algorithms exploit a fundamental connection between gradients and expectations, which allows us to derive efficient algorithms. These algorithms are easy to implement with or without automatic differentiation software. We motivate the development of our framework with several cautionary tales of previous research, which has developed numerous inefficient algorithms for computing expectations and their gradients. We demonstrate how our framework efficiently computes several quantities with known algorithms, including the expected attachment score, entropy, and generalized expectation criteria. As a bonus, we give algorithms for quantities that are missing in the literature, including the KL divergence. In all cases, our approach matches the efficiency of existing algorithms and, in several cases, reduces the runtime complexity by a factor of the sentence length. We validate the implementation of our framework through runtime experiments. We find our algorithms are up to 15 and 9 times faster than previous algorithms for computing the Shannon entropy and the gradient of the generalized expectation objective, respectively.
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